Second seed Jankovic registered a 7-5 6-4 win over Australia's Dellacqua to reach the title match at Hilton Lakes Tennis & Sports Club in Dallas.
The former world number one brought up six break point opportunities and took four of them on her way to wrapping up victory in an hour and 42 minutes.
Vinci, the third seed, hammered Jankovic's fellow Serb Jovanovski 6-0 6-0 to book her place in the final.
The Italian, seeking her first title of the season, was imperious as she dished out a humbling double-bagel to keep alive her hopes of securing a seventh career WTA event victory.
Jankovic and Vinci have met three times before, with the Serb victorious on all three occasions.
The Texas Open serves as a warm-up for the US Open in New York, which starts on Monday.